The standard Latin alphabet contains 26 letters, which means that there are (26*2)^8=5.346*10^13 8-letters, case-sensitive passwords.
The Danish alphabet, as an example of Latin alphabet with additional characters, contains 29 letters, which means there are (29*2)^8=4.308*10^17 8-letters, case-sensitive passwords.
As you can see, adding three letters in the alphabet can increase the number of possible combinations by a very significant factor (in this case, ~ 10,000).
As usual, there are a few catches.
1) If the website accepts your password, but strips the special characters, your approach is useless (thanks Samuel Shifterovich).
2) Don't think that an attacker could never guess that your password is, say, indløse just because it contains a special character. Whatever language you use, a single word from a dictionary will be easily found.